Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, spent by residents driving to work. City Los Angeles Pittsburgh Washington Population N Driving time T 16.8 6489 1804 12.6 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. (a) Construct a power model of driving time in minutes as a function of population measured in thousands. (Round regression parameters to two decimal places.) T = 3,40 x N0.18 T= 1.26 x N1.45 T= 6.84 x N0.87 T= 2.47 x N1.53 T= 4.53 x N0.26 (b) Is average driving time in Pittsburgh more or less than would be expected from its population? (Use the model found in part (a).) more than expected o less than expected (c) If you wish to move to a smaller city to reduce your average driving time to work by 15%, how much smaller should the city be? (Use the model found in part (a). Round your answer to two decimal places.)
Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, spent by residents driving to work. City Los Angeles Pittsburgh Washington Population N Driving time T 16.8 6489 1804 12.6 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. (a) Construct a power model of driving time in minutes as a function of population measured in thousands. (Round regression parameters to two decimal places.) T = 3,40 x N0.18 T= 1.26 x N1.45 T= 6.84 x N0.87 T= 2.47 x N1.53 T= 4.53 x N0.26 (b) Is average driving time in Pittsburgh more or less than would be expected from its population? (Use the model found in part (a).) more than expected o less than expected (c) If you wish to move to a smaller city to reduce your average driving time to work by 15%, how much smaller should the city be? (Use the model found in part (a). Round your answer to two decimal places.)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.3: Modeling Data With Power Functions
Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...
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Transcribed Image Text:Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, spent by residents driving to work.
Population N
City
Los Angeles
Pittsburgh
Washington
Driving time T
6489
16.8
1804
12.6
1808
14.3
Hutchinson
38
6.1
Nashville
347
10.8
Tallahassee
48
7.3
An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population.
(a) Construct a power model of driving time in minutes as a function of population measured in thousands. (Round regression parameters to two decimal places.)
OT = 3.40 x Nº.18
OT = 1.26 x N1.45
T = 6.84 ×
NO.87
OT = 2.47 x N.53
T = 4.53 x
x NO.26
(b) Is average driving time in Pittsburgh more or less than would be expected from its population? (Use the model found in part (a).)
o more than expected
lo less than expected
(c) If you wish to move to a smaller city to reduce your average driving time to work by 15%, how much smaller should the city be? (Use the model found in part (a). Round your answer to two decimal places.)
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